Once you have a job as a zookeeper, you have pretty great odds of sticking around for a long time… as long as you don’t slack. You will have specific knowledge of your animals. Your daily interactions are, as Beyoncé sings, irreplaceable.
Make sure you don’t get sick, attacked, or lazy. Otherwise, you can plan on a long career. You might bounce from zoo to zoo, or you might shift into a more instructional role as you age. Ultimately, it will be your call.